Algebraic-Geometric Codes

✍ Scribed by Tsfasman M.A., Vladut S.G

• Publisher: Springer;Kluwer
• Year: 1991
• Tongue: English
• Leaves: 671
• Series: Mathematics and its applications / Soviet Series 58
• Edition: Softcover reprint of the original 1st ed. 1991
• Category: Library

✦ Synopsis

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series

✦ Table of Contents

Front Matter....Pages i-xxiv
Front Matter....Pages 1-4
Codes and Their Parameters....Pages 5-35
Examples and Constructions....Pages 37-65
Asymptotic Problems....Pages 67-91
Back Matter....Pages 92-94
Front Matter....Pages 95-100
Algebraic Curves....Pages 101-139
Riemann-Roch Theorem....Pages 141-167
Rational Points....Pages 169-190
Elliptic Curves....Pages 191-213
Singular Curves....Pages 215-232
Reductions and Schemes....Pages 233-255
Back Matter....Pages 256-259
Front Matter....Pages 261-264
Constructions and Properties....Pages 265-296
Examples....Pages 297-329
Decoding....Pages 331-347
Asymptotic Results....Pages 349-385
Back Matter....Pages 386-388
Front Matter....Pages 389-393
Codes on Classical Modular Curves....Pages 395-434
Codes on Drinfeld Curves....Pages 435-469
Polynomiality....Pages 471-510
Back Matter....Pages 511-513
Front Matter....Pages 515-518
Definitions and Examples....Pages 519-537
Asymptotically Dense Packings....Pages 539-549
Number Fields....Pages 551-566
Analogues of AG-Codes....Pages 567-593
Back Matter....Pages 594-596
Back Matter....Pages 597-667

✦ Subjects

Algebraische Geometrie;SWD-ID: 40011616;Fehlerkorrekturcode;SWD-ID: 41249173